Problem 74 - Elementary Algebra

Question

Simplify \(\left|-\left(4^{2}+2^{2}-3^{2}\right)\right|\).

Step-by-Step Solution

Answer

Answer: The simplified expression is 11.

Step 1: Evaluate the terms inside the parentheses

Here, we have three terms inside the parentheses: \(4^{2}\), \(2^{2}\), and \(3^{2}\). Let's find their values: \(4^2 = 4 * 4 = 16\) \(2^2 = 2 * 2 = 4\) \(3^2 = 3 * 3 = 9\) Now, we can replace the terms in the expression: \(-\left(4^{2}+2^{2}-3^{2}\right) = -(16 + 4 - 9)\)

Step 2: Perform the operations inside the parentheses

Now, we need to perform the operations inside the parentheses: \(16 + 4 - 9 = 20 - 9 = 11\) Then, replace the result in the expression: \(-(16 + 4 - 9) = -11\)

Step 3: Calculate the absolute value

Finally, calculate the absolute value of \(-11\): \(\left|{-11}\right| = 11\) So, the simplified expression is \(\left|-\left(4^{2}+2^{2}-3^{2}\right)\right| = 11\).